The sign problem is one of the central obstacles to efficiently simulating quantum many-body systems. It is commonly believed that some phases of matter, such as the double semion model, have an intrinsic sign problem and can never be realized in a local sign problem-free Hamiltonian due to the nonpositivity of the wave function. We show that this is not the case. Despite not being stoquastic, the standard criteria for the existence of a sign problem, the double semion model, and all twisted quantum double phases of matter for finite groups $\mathcal{G}$ can be realized in local Hamiltonians that are sign problem-free within a stochastic series expansion. The lack of a sign problem is not fine-tuned and does not require the Hamiltonian to be exactly solvable, with sign problem-free perturbations allowing access to a variety of topological phase transitions.

Close

PrevNext

View figure in article

• Anyons
• Topological order
• Gauge symmetries
• Monte Carlo methods